Orthogonality relations for the primitives of Legendre polynomials and their applications to some spectral problems for differential operators

DOI10.1134/S0001434621090194zbMath1497.33012OpenAlexW3208468237MaRDI QIDQ2666619

T. A. Garmanova, I. A. Sheipak

Publication date: 23 November 2021

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434621090194

zbMATH Keywords

Jacobi matrixleast and greatest eigenvalueprimitives of Legendre polynomials

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General spectral theory of ordinary differential operators (34L05) Eigenvalue problems for linear operators (47A75)

Cites Work

• On properties of integrals of the Legendre polynomial
• Sharp estimates for derivatives of functions in the Sobolev classes \(\overset{\circ} {W}_{2}^r (-1,1)\)
• Spectral asymptotics for problems with integral constraints
• On exact constants in some embedding theorems of high order
• On the symmetry of extremal in several embedding theorems
• Estimates of derivatives in Sobolev spaces in terms of hypergeometric functions
• On sharp estimates of even-order derivatives in Sobolev spaces
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